Subgroups — C₁₁×C₁₃×#1039 #28384691

Order 14300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₃×Dic₅	—	5	6	no	maximal
4	C₂×C₅×C₁₁×C₁₃	D₅	1	6	yes	—
5	C₁₃×#1039	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×#1039	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₃	Dic₅	1	6	yes	complemented
8	C₂×C₅²×C₁₃	C₂×C₁₁	1	1	yes	characteristic
9	C₄×C₁₁×C₁₃	—	25	1	no	Hall
10	C₂×C₅²×C₁₁	C₂×C₁₃	1	1	yes	characteristic
11	C₅²×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅²×C₁₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×Dic₅	—	5	6	no	—
15	C₁₁×Dic₅	—	5	6	no	—
16	C₁₁×C₁₃	#1039	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₃	D₅×C₁₁	1	6	yes	—
18	C₂×C₅×C₁₁	D₅×C₁₃	1	6	yes	—
19	#1039	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	C₁₁×Dic₅	1	6	yes	complemented
21	C₅×C₁₁	C₁₃×Dic₅	1	6	yes	complemented
22	C₄×C₁₃	—	25	1	no	Hall
23	C₂×C₅²	C₂×C₁₁×C₁₃	1	1	yes	characteristic
24	C₄×C₁₁	—	25	1	no	Hall
25	C₂×C₁₃	C₁₁×C₅⋊D₅	1	1	yes	characteristic
26	C₅²	C₄×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	C₁₃×C₅⋊D₅	1	1	yes	characteristic
28	Dic₅	—	5	6	no	—
29	C₁₃	C₁₁×#1039	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₁₃×#1039	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	D₅×C₁₁×C₁₃	1	6	yes	—
32	C₅	C₁₁×C₁₃×Dic₅	1	6	yes	complemented
33	C₄	—	25	1	no	Sylow
34	C₂	C₁₁×C₁₃×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	C₅⋊D₅
commutator, hypocenter	C₅²	C₄×C₁₁×C₁₃
Frattini	C₂	C₁₁×C₁₃×C₅⋊D₅
Fitting, socle, prime radical	C₂×C₅²×C₁₁×C₁₃	C₂
cosocle	C₂×C₅²	C₂×C₁₁×C₁₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₃	C₄	semidirect
5. C₁₃×#1039	C₁₁	direct (N × H)
6. C₁₁×#1039	C₁₃	direct (N × H)
7. C₅×C₁₁×C₁₃	Dic₅	semidirect
11. C₅²×C₁₃	C₄×C₁₁	semidirect
13. C₅²×C₁₁	C₄×C₁₃	semidirect
16. C₁₁×C₁₃	#1039	direct (N × H)
19. #1039	C₁₁×C₁₃	direct (N × H)
20. C₅×C₁₃	C₁₁×Dic₅	semidirect
21. C₅×C₁₁	C₁₃×Dic₅	semidirect
26. C₅²	C₄×C₁₁×C₁₃	semidirect
29. C₁₃	C₁₁×#1039	direct (N × H)
30. C₁₁	C₁₃×#1039	direct (N × H)
32. C₅	C₁₁×C₁₃×Dic₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅²×C₁₁×C₁₃	2
C₁₁×C₁₃×Dic₅	5
C₁₃×#1039	11
C₁₁×#1039	13

Subgroups — C11×C13×#1039 #28384691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×#1039 #28384691